*. and ?. Outbounds, e' 1 * t ? Outbounds

*. and +. Outbounds, e' 1 * t ? Outbounds

. Maxoccurs, Message"Operation"t

*. and ?. Outbounds, e' 1 * t ? Outbounds

D. Cette-expression, une incompatibilité de type One-to-One + est détectée entre une transition t sortante de l'état e de I et une transition t' sortante de l'état e' de I'

M. , M. One-'xor-"-one, and M. Many-'l, One M to M One' XOR "Many M to M One'L [3] K"One M to M One' XOR "One P M to M One'L [4] K"One M to M One' XOR "One M to M One P 'L [5] K"One M to M Many' XOR "Many M to M One'L [6] K"One M to M Many' XOR "One P M to M One'L [7] K"One M to M Many' XOR "One M to M One, Many M to M One' XOR "One P M to M One'L [9

. Qu, une expression One M to M One et une autre One M to M Many soient vraies en même temps pour une même paire d'états. On en déduit que: (One-to-One) XOR (One-to-Many)

D. Complétude-de-chaque-expression, on dit d'un objet mathématique qu'il est complet pour exprimer que rien ne peut lui être ajouté, et ce dans un sens qu'il faut préciser dans chaque contexte

. Dans-notre-contexte, une expression de détection d'un patron d'incompatibilité est dite complète, quand elle couvre tous les cas de l'incompatibilité qu'elle modélise. Ainsi, chacune des expressions de détection des incompatibilités présentées à la section 4

. Aussi, One M to M Many est vérifiée pour toutes les incompatibilités dues à une correspondance entre une opération d'un service, et plusieurs opérations d'un autre service. Pour démontrer la complétude de chacune de nos expressions

. Preuve-de-la-complétude-de-l, expression One-to-One: Supposons qu'il existe une incompatibilité de type One-to-One (noté E) entre deux transitions t et t' pour laquelle l'expression booléenne modélisant l'incompatibilité de type One-to-One est non-vérifié, Cela veut dire que sa négation (¬E) est vérifiée

. Ag, Message(Operation(i

. Notons, que les n messages sont de même type Type(Message(Operation(i

L. Enfin and . Ligne, 8 spécifie la dernière transistion de l'opérateur permettant d'envoyer au destinaire le message obtenu par l'agrégation ci-dessus

+. L. One, opérateur consiste à consommer un message sous forme d'une liste de n éléments du même type, provenant d'un service émetteur. Tant que la liste est non-vide, envoyer sa tête à l'action correspondante dans l'interface du service récepteur

B. Aït-bachir, ArchiMed : un canevas pour la détection et la résolution des incompatibilités des conversations entre services Web, Thèse de doctorat en informatique, 2008.

M. [. Aït-bachir and . Fauvet, Un médiateur pour la réconciliation de conversations entre services web, INFORSID, pp.537-552, 2007.

G. Alonso, F. Casati, H. Kuno, and V. Machiraju, Web Services -Concepts, Architectures and Applications, pp.8-30, 2004.

A. [. Aragão and . Fernandes, Conflict Resolution in Web Service Federations
DOI : 10.1007/978-3-540-39872-1_10

V. De-antonellis, M. Melchiori, and P. Plebani, An approach to Web Service compatibility in cooperative processes, 2003 Symposium on Applications and the Internet Workshops, 2003. Proceedings., p.95, 2003.
DOI : 10.1109/SAINTW.2003.1210134

G. Athanasopoulos, A. Tsalgatidou, and M. Pantazoglou, Interoperability among Heterogeneous Services, 2006 IEEE International Conference on Services Computing (SCC'06), pp.174-181, 2006.
DOI : 10.1109/SCC.2006.59

. [. Claro, SPOC -Un canevas pour la composition automatique de services web dédiés à la réalisation de devis, Thèse de Doctorat, Ecole Doctorale d'Angers, 2006.

B. Benatallah, F. Casati, D. Grigori, H. R. Motahari-nezhad, and F. Toumani, Developing adapters for web services integration Web service interfaces, Proceedings of the 17th International Conference on Advanced Information System Engineering, CAiSE Proceedings of the 14th international conference on World Wide Web, WWW, pp.415-429, 2005.

B. Benatallah, F. Casati, and F. Toumani, Representing, analysing and managing Web service protocols, Data & Knowledge Engineering, vol.58, issue.3, pp.327-357, 2006.
DOI : 10.1016/j.datak.2005.07.006

URL : https://hal.archives-ouvertes.fr/hal-00107196

M. Nezhad, Service mosaic: A model-driven framework for web services life-cycle management, IEEE Internet Computing, vol.10, issue.4, pp.55-63, 2006.

B. Benatallah, R. Dijkman, M. Dumas, and Z. Maamar, Service-Composition, Service-Oriented Software System Engineering: Challenges and Practices. IDEA Group, pp.48-66
DOI : 10.4018/978-1-59140-426-2.ch003

URL : https://hal.archives-ouvertes.fr/hal-00953911

B. Benatallah, M. Dumas, and Q. Sheng, Facilitating the Rapid Development and Scalable Orchestration of Composite Web Services, Distributed and Parallel Databases, vol.17, issue.1, pp.5-37, 2005.
DOI : 10.1023/B:DAPD.0000045366.15607.67

M. [. Benatallah, C. Hacid, F. Rey, and . Toumani, The SemanticWeb-ISWC 2003, chapitre Request Rewriting-Based Web Service Discovery, LNCS, pp.242-257, 2003.

B. [. Bowers and . Ludäscher, An ontology-driven framework for data transformation in scientific workows, International Workshop on Data Integration in the Life Sciences, DILS, pp.1-16, 2004.

M. Berndl, O. Lhotak, F. Qian, L. Hendren, and N. Umanee, Points-to analysis using bdds, Proceedings of the ACM SIGPLAN Conference on Programming Language Design and Implementation, 2003.

D. Benslimane, Z. Maamar, Y. Taher, M. Lahkim, M. C. Fauvet et al., A multi-layer and multiperspective approach to compose web services, Proceedings of the 21st International Conference on Advanced Networking and Applications, AINA, pp.31-37, 2007.

R. [. Brogi and . Popescu, Automated Generation of BPEL Adapters, Proceedings of the 4 th International Conference on Service Oriented Computing, ICSOC, pp.27-39, 2006.
DOI : 10.1007/11948148_3

L. Bordeaux, G. Salaün, D. Berardi, and M. Mecella, When are Two Web Services Compatible?, Proceedings of the 5th International Conference on Technologies for E-Services, pp.15-28, 2004.
DOI : 10.1007/978-3-540-31811-8_2

B. Benatallah, Q. Z. Sheng, and M. Dumas, The Self-Serv environment for Web services composition, IEEE Internet Computing, vol.7, issue.1, pp.40-48, 2003.
DOI : 10.1109/MIC.2003.1167338

C. Bussler, Semantic Web services: reflections on Web service mediation and composition, Proceedings of the 7th International Conference on Properties and Applications of Dielectric Materials (Cat. No.03CH37417), pp.253-260
DOI : 10.1109/WISE.2003.1254489

K. M. Chandy, M. Charpentier, and A. Capponi, Towards a theory of events, Proceedings of the 2007 inaugural international conference on Distributed event-based systems , DEBS '07, pp.180-187, 2007.
DOI : 10.1145/1266894.1266929

J. [. Cabral and . Domingue, Mediation of Semantic Web Services in IRS-III, Proceedings of the Workshop on Mediation in Semantic Web Services in conjunction with the 3rd International Conference on Service Oriented Computing, 2005.

P. [. Claro, J. K. Albers, and . Hao, Selecting web services for optimal composition, Procedings of the 2005 International Conference on Web Services, ICWS, 2005.

M. Chanliau, Web services security: What's required to secure a service oriented architecture, 2006.

J. [. Chae, J. H. Lee, and . Bae, AN APPROACH TO CHECKING BEHAVIORAL COMPATIBILITY BETWEEN WEB SERVICES, International Journal of Software Engineering and Knowledge Engineering, vol.18, issue.02, pp.223-241, 2008.
DOI : 10.1142/S0218194008003647

K. Czajkowski, I. Foster, and C. Kesselman, Agreement-Based Resource Management, Proceedings of the IEEE, pp.631-643, 2005.
DOI : 10.1109/JPROC.2004.842773

Y. [. Derong, Y. Ge, N. Nan, and . Tiezheng, Heterogeneity resolution based on ontology in web services composition, Proceedings of the Workshop on E- Commerce Technology for Dynamic E-Business, pp.274-277, 2004.

X. Dong, A. Halevy, J. Madhavan, E. Nemes, and J. Zhang, Similarity Search for Web Services, Proceedings of the Thirtieth international conference on Very large data bases, VLDB, pp.372-383, 2004.
DOI : 10.1016/B978-012088469-8.50035-8

M. Dumas, M. Spork, and K. Wang, Adapt or Perish: Algebra and Visual Notation for Service Interface Adaptation, Procedings of the 4 th International Conference on Business Process Management, BPM, number 4102 in LNCS, pp.65-80, 2006.
DOI : 10.1007/11841760_6

M. D. Ernst, R. Lencevicius, and J. H. Perkins, Detection of web service substitutability and composability. International Workshop on Web Services - Modeling and Testing, WS-MaTe, pp.123-135, 2006.

M. C. Fauvet, H. Duarte, M. Dumas, and B. Benatallah, Handling Transactional Properties in Web Service Composition, '05 The 6th International Conference on Web Information Systems Engineering, pp.20-22, 2005.
DOI : 10.1007/11581062_21

URL : https://hal.archives-ouvertes.fr/hal-00953911

M. C. Fauvet, H. Duarte, Y. Taher, and D. Benslimane, Sélection dynamique de services web -une approche à base de communautés, INFORSID, pp.505-520, 2007.

M. Fuchs, Adapting Web services in a heterogeneous environment, Proceedings. IEEE International Conference on Web Services, 2004., pp.656-664, 2004.
DOI : 10.1109/ICWS.2004.1314794

H. Foster, S. Uchitel, J. Magee, and J. Kramer, Compatibility verification for Web service choreography, Proceedings. IEEE International Conference on Web Services, 2004., pp.738-741, 2004.
DOI : 10.1109/ICWS.2004.1314806

D. Fensel, F. V. Harmelen, I. Horrocks, D. L. Mcguinness, and P. F. Patel-schneider, OIL: an ontology infrastructure for the Semantic Web, IEEE Intelligent Systems, vol.16, issue.2, pp.38-45, 2001.
DOI : 10.1109/5254.920598

I. Foster, T. Freeman, K. Keahey, D. Scheftner, B. Sotomayer et al., Virtual Clusters for Grid Communities, Sixth IEEE International Symposium on Cluster Computing and the Grid (CCGRID'06), pp.16-19, 2006.
DOI : 10.1109/CCGRID.2006.108

[. Garcia, M. De, and . Toledo, Semantics-enriched QoS policies for web service interactions, Proceedings of the 12th Brazilian symposium on Multimedia and the web , WebMedia '06, pp.35-44, 2006.
DOI : 10.1145/1186595.1186601

M. [. Gouscos, P. Kalikakis, and . Georgiadis, An approach to modeling web service QoS and provision price, Fourth International Conference on Web Information Systems Engineering Workshops, 2003. Proceedings., pp.121-130, 2003.
DOI : 10.1109/WISEW.2003.1286794

A. Haller, E. Cimpian, A. Mocan, E. Oren, and C. Bussler, WSMX - a semantic service-oriented architecture, IEEE International Conference on Web Services (ICWS'05), pp.321-328, 2005.
DOI : 10.1109/ICWS.2005.139

A. Haller, E. Cimpian, A. Mocan, E. Oren, and C. Bussler, WSMX - a semantic service-oriented architecture, IEEE International Conference on Web Services (ICWS'05), pp.321-328, 2005.
DOI : 10.1109/ICWS.2005.139

. [. Hofstede, Yawl : yet another workow language, Information Systems, vol.30, pp.245-275, 2005.

J. Y. Jung, W. Hur, S. Kang, and H. Kim, Business process choreography for b2b collaboration, IEEE Internet Computing, vol.8, issue.1, pp.37-45, 2004.
DOI : 10.1109/MIC.2004.1260702

N. Jain, S. Mishra, A. Srinivasan, J. Gehrke, J. Widom et al., Towards a streaming SQL standard, Proceedings of the international conference on Very large data bases, VLDB, pp.1379-1390, 2008.
DOI : 10.14778/1454159.1454179

T. Kawamura, J. Blasio, T. Hasegawa, M. Paolucci, and K. Sycara, Public Deployment of Semantic Service Matchmaker with UDDI Business Registry, Proceedings of the 3rd International Semantic Web Conference (ISWC2004), pp.752-766, 2004.
DOI : 10.1007/978-3-540-30475-3_52

S. [. Kalepu, S. W. Krishnaswamy, and . Loke, Reputation = f(user ranking, compliance, verity), Proceedings. IEEE International Conference on Web Services, 2004., pp.200-2007, 2004.
DOI : 10.1109/ICWS.2004.1314740

S. [. Krishnaswamy, A. B. Loke, and . Zaslavsky, Application run time estimation, Proceedings of the 2002 ACM symposium on Applied computing , SAC '02, pp.1153-1159, 2002.
DOI : 10.1145/508791.509016

H. [. Kaminski, M. Müller, and . Litoiu, A design for adaptive web service evolution, Proceedings of the 2006 international workshop on Self-adaptation and self-managing systems , SEAMS '06, pp.86-92, 2006.
DOI : 10.1145/1137677.1137694

A. [. Kashyap and . Sheth, Semantic and schematic similarities between database objects: a context-based approach, The VLDB Journal The International Journal on Very Large Data Bases, vol.5, issue.4, pp.276-304, 1996.
DOI : 10.1007/s007780050029

W. Kongdenfha, R. Saint-paul, B. Benatallah, and F. Casati, An Aspect-Oriented Framework for Service Adaptation, Proceedings of the 4 th International Conference on Service Oriented Computing, ICSOC, pp.15-26, 2006.
DOI : 10.1007/11948148_2

B. Lin, N. Gu, and Q. Li, A Requester-based Mediation Framework for Dynamic Invocation of Web Services, 2006 IEEE International Conference on Services Computing (SCC'06), pp.445-454, 2006.
DOI : 10.1109/SCC.2006.13

H. [. Li and . Jagadish, Compatibility determination in web services, ICEC Workshop on on E-Government and Web Services, 2003.

T. Ledoux, J. Noyé, J. Menaud, M. Blay-fornarino, D. Caromel et al., Etat de l'art sur l'adaptabilité, 2001.

Y. Liu, A. H. Ngu, and L. Z. Zeng, QoS computation and policing in dynamic web service selection, Proceedings of the 13th international World Wide Web conference on Alternate track papers & posters , WWW Alt. '04, pp.66-73, 2004.
DOI : 10.1145/1013367.1013379

J. [. Luo and . Li, A Web Services Provisioning Optimization Model in a Web Services Community, IEEE International Conference on e-Business engineering, pp.689-696, 2005.

F. Liu, Y. Shi, L. Zhang, L. Lin, and B. Shi, Analysis of web services composition and substitution via ccs. Data Engineering Issues in E-Commerce and Services, DEECS, pp.236-245, 2006.

S. [. Mandell and . Mcilraith, The Semantic Web -ISWC 2003, chapitre Adapting BPEL4WS for the Semantic Web : The Bottom-Up Approach to Web Service Interoperation, LNCS, pp.224-241, 2003.

B. Medjahed and A. Bouguettaya, A dynamic foundational architecture for semantic web services. Distributed and Parallel Databases, pp.179-206, 2005.

K. Srinivasan and . Sycara, DAML-S (and OWL-S) 0.9 draft release, 2003.

. [. Milner, A calculus of communicating systems, 1980.
DOI : 10.1007/3-540-10235-3

A. Martens, S. Moser, A. Gerhardt, and K. Funk, Analyzing Compatibility of BPEL Processes, Advanced Int'l Conference on Telecommunications and Int'l Conference on Internet and Web Applications and Services (AICT-ICIW'06), p.147, 2006.
DOI : 10.1109/AICT-ICIW.2006.48

M. Mecella, B. Pernici, and P. Craca, Compatibility of e -Services in a cooperative multi-platform environment, Proceedings of the Second International Workshop on Technologies for E-Services, TES, pp.44-57, 2001.

. [. Mrissa, Médiation Sémantique Orientée contexte pour la composition de services Web, Thèse de doctorat en informatique, 2007.

Z. Maamar, Q. Z. Sheng, and D. Benslimane, Sustaining Web Services High-Availability Using Communities, 2008 Third International Conference on Availability, Reliability and Security, pp.834-841, 2008.
DOI : 10.1109/ARES.2008.7

K. [. Miller, P. Verma, A. Rajasekaran, R. Sheth, K. Aggarwal et al., WSDL-S: Adding Semantics to WSDL -White Paper, 2004.

H. R. Motahari-nezhad, B. Benatallah, F. Casati, and F. Toumani, Web Services Interoperability Specifications, Computer, vol.39, issue.5, pp.24-32, 2006.
DOI : 10.1109/MC.2006.181

H. R. Motahari-nezhad, B. Benatallah, A. Martens, F. Curbera, and F. Casati, Semi-automated adaptation of service interactions, Proceedings of the 16th international conference on World Wide Web , WWW '07, pp.993-1002, 2007.
DOI : 10.1145/1242572.1242706

S. Narayanan and S. Mcilraith, Analysis and simulation of Web services, Comput. Networks, pp.675-693, 2003.
DOI : 10.1016/S1389-1286(03)00228-7

M. Nagarajan, K. Verma, A. P. Sheth, J. Miller, and J. Lathem, Semantic Interoperability of Web Services - Challenges and Experiences, 2006 IEEE International Conference on Web Services (ICWS'06), pp.373-382, 2006.
DOI : 10.1109/ICWS.2006.116

[. Uddi, Discovery and Integration version 3, 2009.

H. Paik, B. Benatallah, and F. Toumani, WS-CatalogNet: Building Peer-to-Peer e-Catalog, 6th International Conference on Flexible Query Answering Systems, pp.256-269, 2004.
DOI : 10.1007/978-3-540-25957-2_21

P. F. Pires, M. R. Benevides, and M. Mattoso, Mediating heterogeneous Web services, 2003 Symposium on Applications and the Internet, 2003. Proceedings., pp.344-347, 2003.
DOI : 10.1109/SAINT.2003.1183068

A. [. Ponnekanti and . Fox, Interoperability Among Independently Evolving Web Services, Proceedings of the 5th ACM International Conference on Middleware, pp.331-351, 2004.
DOI : 10.1007/BFb0053382

M. Paolucci, T. Kawamura, T. R. Payne, and K. P. Sycara, Semantic Matching of Web Services Capabilities, de Lecture Notes in Computer Science, First International Semantic Web Conference, pp.333-347, 2002.
DOI : 10.1007/3-540-48005-6_26

A. [. Radetzki and . Cremers, IRIS: a framework for mediator-based composition of service-oriented software, Proceedings. IEEE International Conference on Web Services, 2004., pp.752-756, 2004.
DOI : 10.1109/ICWS.2004.1314809

S. [. Spencer and . Liu, Inferring Data Transformation Rules to Integrate Semantic Web Services, Proceedings of the International Semantic Web Conference, IWSC, pp.456-470, 2004.
DOI : 10.1007/978-3-540-30475-3_32

Q. Z. Sheng, Z. Maamar, J. Yu, and A. H. Ngu, Robust Web Services Provisioning through On-Demand Replication, Proceedings of the Third International United Information Systems Conference, UNISCON, pp.4-16, 2009.
DOI : 10.1109/MC.2007.400

A. [. Taher, M. C. Aït-bachir, D. Fauvet, and . Benslimane, Diagnosing Incompatibilities in Web Service Interactions for Automatic Generation of Adapters, 2009 International Conference on Advanced Information Networking and Applications, 2009.
DOI : 10.1109/AINA.2009.118

URL : https://hal.archives-ouvertes.fr/hal-00953846

Y. Taher, D. Benslimane, M. C. Fauvet, and Z. Maamar, Towards an Approach forWeb services Substitution, 2006 10th International Database Engineering and Applications Symposium (IDEAS'06), pp.166-173, 2006.
DOI : 10.1109/IDEAS.2006.45

S. [. Tolk and . Diallo, Model-based Data Engineering for Web Services, IEEE Internet Computing, vol.9, issue.4, 2005.

Y. Taher, M. C. Fauvet, M. Dumas, and D. Benslimane, Using CEP technology to adapt messages exchanged by web services, Proceeding of the 17th international conference on World Wide Web , WWW '08, pp.1231-1232, 2008.
DOI : 10.1145/1367497.1367741

URL : https://hal.archives-ouvertes.fr/hal-00953871

S. [. Williams, J. E. Battle, and . Cuadrado, Protocol mediation for adaptation in semantic web services. The Semantic Web: Research and Applications, pp.635-649, 2006.

E. Wu, Y. Diao, and S. Rizvi, High-performance complex event processing over streams, Proceedings of the 2006 ACM SIGMOD international conference on Management of data , SIGMOD '06, pp.407-418, 2006.
DOI : 10.1145/1142473.1142520

P. [. Wombacher, B. Fankhauser, E. Mahleko, and . Neuhold, Matchmaking for business processes based on choreographies, IEEE International Conference on e-Technology, e-Commerce and e-Service, 2004. EEE '04. 2004, pp.359-368, 2004.
DOI : 10.1109/EEE.2004.1287334

E. [. Wang and . Stroulia, Flexible interface matching for web-service discovery, Proceedings of the Fourth International Conference on Web Information Systems Engineering, WISE, pp.147-156, 2003.

J. Wu and Z. Wu, Similarity-based web service matchmaking, Proceedings of the 2005 IEEE International Conference on Services Computing, SCC, pp.287-294, 2005.

T. Yu, Y. Zhang, and K. J. Lin, Modeling and measuring privacy risks in qos web services, Proceedings of the Third International Conference Enterprise Computing, E-Commerce, and E-Services, CEC-EEE, pp.4-4, 2006.

W. Zahereddine and Q. Mahmoud, A Framework for Automatic and Dynamic Composition of Personalized Web Services, AINA, 19th International Conference on Advanced Information Networking and Applications, pp.28-30, 2005.

J. Z. Zhang, S. J. Yu, X. K. Ge, and G. Wu, Automatic web service composition based on service interface description, Proceedings of the International Conference on Internet Computing, pp.120-126, 2006.